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arXiv 2602.02009cs.LG
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逻辑引导的向量场用于约束生成建模

Logic-Guided Vector Fields for Constrained Generative Modeling

Rochester Institute of Technology(罗切斯特理工学院)

Ali Baheri

AI总结:

提出逻辑引导向量场(LGVF)框架,通过可微逻辑约束松弛注入流匹配生成模型,结合训练时逻辑损失和推理时梯度调整,在三个约束生成案例中减少59-82%的约束违反。

摘要:

神经符号系统旨在结合符号逻辑的表达结构与神经学习的灵活性;然而,生成模型通常缺乏在生成时强制执行声明性约束的机制。我们提出了逻辑引导向量场(LGVF),这是一个神经符号框架,将符号知识(指定为逻辑约束的可微松弛)注入流匹配生成模型。LGVF耦合了两种互补机制:(1)训练时逻辑损失,惩罚连续流轨迹上的约束违反,权重强调目标分布附近的正确性;(2)推理时调整,使用约束梯度引导采样,作为对学习动力学的轻量级、逻辑信息校正。我们在三个约束生成案例研究上评估了LGVF,涵盖线性、非线性和多区域可行性约束。在所有设置中,与标准流匹配相比,LGVF将约束违反减少了59-82%,并在每种情况下实现了最低的违反率。在线性和环形设置中,LGVF还通过MMD衡量提高了分布保真度,而在多障碍物设置中,我们观察到满意度-保真度权衡,可行性提高但MMD增加。除了定量收益外,LGVF还产生了具有约束意识的向量场,表现出新兴的避障行为,无需显式路径规划即可将样本绕过禁止区域。

英文摘要:

Neuro-symbolic systems aim to combine the expressive structure of symbolic logic with the flexibility of neural learning; yet, generative models typically lack mechanisms to enforce declarative constraints at generation time. We propose Logic-Guided Vector Fields (LGVF), a neuro-symbolic framework that injects symbolic knowledge, specified as differentiable relaxations of logical constraints, into flow matching generative models. LGVF couples two complementary mechanisms: (1) a training-time logic loss that penalizes constraint violations along continuous flow trajectories, with weights that emphasize correctness near the target distribution; and (2) an inference-time adjustment that steers sampling using constraint gradients, acting as a lightweight, logic-informed correction to the learned dynamics. We evaluate LGVF on three constrained generation case studies spanning linear, nonlinear, and multi-region feasibility constraints. Across all settings, LGVF reduces constraint violations by 59-82% compared to standard flow matching and achieves the lowest violation rates in each case. In the linear and ring settings, LGVF also improves distributional fidelity as measured by MMD, while in the multi-obstacle setting, we observe a satisfaction-fidelity trade-off, with improved feasibility but increased MMD. Beyond quantitative gains, LGVF yields constraint-aware vector fields exhibiting emergent obstacle-avoidance behavior, routing samples around forbidden regions without explicit path planning.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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